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Some years ago, I read the Newton biography "Never at Rest" by Richard Westfall. However, I don't currently have access to a copy, so the following is from memory.

According to the biography, Newton has no formal mathematical background to speak of, nor was there really much by way of mathematical background to be had at the time his career began. However, after becoming a student at Cambridge, it took him approximately 18 months, from a standing start, surrounded by a whole lot of nothing (ie. mid-seventeenth century Cambridge) to start making original mathematical discoveries, including the Binomial Theorem, and the early stages of the calculus. Much of this work emerged from things like formal polynomial manipulation.

His background was essentially his own reading of people like Descartes, and Fermat.

My recollection is that the main historical record of this is his notebook (called by him, his "waste" book), which was given to him by his stepfather, Barnabas Smith. But it is unclear to me how historians know what period the notes therein were made.

The upshot is, I'm wondering if my description above is still the standard understanding of the Newton mathematics chronology, or at the least the beginning of the chronology.

The description given above just seems a little improbable. It seems more likely to me that such substantial mathematical advances came at a later period of his life, and with more effort than would be suggested by an 18 month run up from a standing start to original mathematical discoveries.

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    $\begingroup$ Newton's mathematical works are available on the Internet with commentaries. Did you look at those? I don't think his background was limited to reading Fermat and Descartes. It was much larger than this, and one of his teachers was an outstanding mathematician Barrow. $\endgroup$ – Alexandre Eremenko Sep 8 '15 at 21:37
  • $\begingroup$ I'm not asking about his mathematical works. I'm asking about his mathematical development. And what were the other people he read? In any case, he would have had little time for study preceding his original mathematical work, if the chronology I quoted is accurate. $\endgroup$ – Faheem Mitha Sep 8 '15 at 21:40
  • $\begingroup$ The commentaties to his mathematical works address these questions. We cannot know for sure what he read. $\endgroup$ – Alexandre Eremenko Sep 8 '15 at 21:57
  • $\begingroup$ Here is a reasonable source: maa.org/sites/default/files/pdf/upload_library/22/Polya/… It specially addresses what he read. $\endgroup$ – Alexandre Eremenko Sep 8 '15 at 22:05
  • $\begingroup$ @AlexandreEremenko Thank you for the link - it is an interesting read. $\endgroup$ – Faheem Mitha Sep 8 '15 at 22:14
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This paper https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020729.02p0067y.pdf

addresses the question. Comprehensive commentaries of Whiteside to Mathematical Papers of Newton give more details.

The most important authors Newton read in his young age were Euclid, Descartes, Oughtred, Schooten, Viete and Wallis. He was in personal contact with another outstanding mathematician, Barrow.

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  • $\begingroup$ Is there any information about the time frame in which Newton was in contact with Barrow, or any details about the contact? What about other mathematicians? $\endgroup$ – Faheem Mitha Sep 9 '15 at 13:15
  • $\begingroup$ There is some scattered information, some in the paper that I linked, some in Arnold's book, "Huygens and Barrow, Newton and Hooke." There is an enormous literature on Newton, all aspects of his life and activities, but all essential information in it comes from his papers and Correspondence, which I prefer as a primary source. $\endgroup$ – Alexandre Eremenko Sep 9 '15 at 20:31
  • $\begingroup$ He was in correspondence with Wallis, Leibniz, Huygens and many other people. With Barrow he could talk because they were in the same university. And Barrow was very fond of Newton: he made him his heir when retired, and gave him his book collection. So I suppose they talked much to each other. $\endgroup$ – Alexandre Eremenko Sep 9 '15 at 20:34
  • $\begingroup$ Yes, I see, but I was thinking more about the early days, when he was an undergraduate. $\endgroup$ – Faheem Mitha Sep 9 '15 at 20:50
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    $\begingroup$ There was no distinction between "undergraduate" and "graduate" in those times:-) And the only sources for those early days are is own and his classmates recollections. $\endgroup$ – Alexandre Eremenko Sep 9 '15 at 21:04

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